On existence of efficient solutions to vector optimization problems in Banach spaces
Peter I. Kogut, Rosanna Manzo, I. V. Nechay · Università del Salento · 2011
In this paper, we present a new characterization of lower semicontinuity of vectorvalued mappings and apply it to the solvability of vector optimization problems in Banach spaces. With this aim we introduce a class of vector-valued mappings that is more wider than the class of vector-valued mappings with the "typical" properties of lower semi-continuity including quasi and order lower semi-continuity. We show that in this case the corresponding vector optimization problems have non-empty sets of efficient solutions.